High Bandwidth Multimode Optical Fiber Optimized for Multimode and Single-Mode Transmissions

ABSTRACT

It is proposed a home optical data network formed of an optical fiber comprising an optical core and an optical cladding surrounding the optical core, the optical core having a refractive graded-index profile with a minimal refractive index n 1  and a maximal refractive index n 0 , said optical fiber being such that it has a numerical aperture NA and an optical core radius a satisfying a criterion C of quality of optical communications defined by the following equation: 
     
       
         
           
             C 
             = 
             
               NA 
               - 
               
                 0.02 
                 × 
                 a 
               
             
           
         
       
       
         
           
             where 
              
             
               : 
             
           
         
       
       
         
           
             
               NA 
               = 
               
                 
                   
                     
                       n 
                       0 
                       2 
                     
                     - 
                     
                       n 
                       1 
                       2 
                     
                   
                 
                 = 
                 
                   
                     
                       
                         n 
                         0 
                       
                       · 
                       
                         
                           2 
                            
                           Δ 
                         
                       
                     
                      
                     
                         
                     
                      
                     with 
                      
                     
                         
                     
                      
                     Δ 
                   
                   = 
                   
                     
                       
                         n 
                         0 
                         2 
                       
                       - 
                       
                         n 
                         1 
                         2 
                       
                     
                     
                       2 
                        
                       
                         n 
                         0 
                         2 
                       
                     
                   
                 
               
             
             , 
           
         
       
     
     Δ is the normalized refractive index difference,
 
and in that said minimal and maximal refractive indexes n 1 , n 0  and said optical core radius a are chosen such that NA&gt;0.20, a&gt;10 μm and |C|&lt;0.20.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation application of U.S. patentapplication Ser. No. 14/418,846, filed Jan. 30, 2015, which is a Section371 National Stage Application of International Application No.PCT/IB2012/002228, filed Oct. 11, 2012, the contents of which are herebyincorporated by reference in their entireties.

FIELD OF THE INVENTION

The invention relates to fiber optic transmission, and, morespecifically, to an optical fiber optimized for supporting bothsingle-mode and multimode transmissions.

TECHNOLOGICAL BACKGROUND

An optical fiber is conventionally constituted of an optical core, whichtransmits an optical signal, and of an optical cladding, which confinesthe optical signal within the optical core. To that end the refractiveindex of the core, n_(c), is greater than the one of the cladding,n_(g). An optical fiber is generally characterized by a refractive indexprofile that associates the refractive index (n) with the radius (r) ofthe optical fiber: the distance r with respect to the center of theoptical fiber is shown on x-axis and the difference between therefractive index at radius r and the refractive index of the opticalcladding is shown on y-axis.

Nowadays, two main categories of optical fibers exist: multimode fibersand single-mode fibers. In a multimode fiber, for a given wavelength,several optical modes are propagated simultaneously along the opticalfiber, whereas in a single-mode fiber, the higher order modes (hereaftercalled HOMs) are cut-off or highly attenuated.

Single-mode fibers are commonly used for long-distance applications,such as access networks. To obtain an optical fiber capable to transmita single-mode optical signal, a core with a relatively small diameter isrequired (typically between 5 μm and 11 μm). To meet requirements ofhigh speed or bit-rate applications (for example 10 Gbps), standardsingle-mode fibers require use of a modulated single-mode laser emittertuned to work typically at a wavelength of 1550 nm.

Multimode fibers are commonly used for short-distance applicationsrequiring a high bandwidth, such as local area networks (LANs) andmulti-dwelling units (MDUs), more generally known as in-buildingnetworks. The core of a multimode fiber typically has a diameter of 50μm, or 62.5 μm. The most prevalent multimode fibers intelecommunications are the refractive graded-index profile opticalfibers. Such a refractive index profile guaranties, by minimizing theintermodal dispersion (i.e. the difference between the propagation delaytimes or group velocity of the optical modes along the optical fiber), ahigh modal bandwidth for a given wavelength.

For the development of an optical home network, the choice of thecategory of optical fiber category is critical. Multimode fiber is acost effective solution for optical data networks. Thanks to their widernumerical aperture and core diameter, and their low modal dispersionprovided by their graded-index core profile, multimode fibers cansupport efficiently 10 Gbps optical signals emitted by cost effectivelight sources based solutions (such as Vertical Cavity Surface EmittingLaser or VCSEL), whereas single-mode fibers require expensive andtolerant single-mode transceivers. In particular, the connection of thelight source with the single-mode fiber (launching conditions) requirestighter alignment tolerances than with the multimode fiber.

However, since the optical home network is expected to be connected tooutside access networks, which mainly use single-mode technology becauseof longer reach requirements, the problem of interoperability withsingle-mode fibers needs further considerations.

In practice, multimode fibers are not designed to be interconnected withsingle-mode transmission systems. A home network can be seen as anetwork of optical fibers that enables the users to connect devices atboth ends of the network. Today, the devices are likely to implementmultimode optical transmission based technologies that require multimodefibers, whilst tomorrow they could be designed to operate also with asingle-mode based technology.

It is therefore desirable to provide a hybrid optical fiber for a homenetwork that can transmit both multimode optical signals at an operatingwavelength of the home network, for example 850 nm, and single-modeoptical signals at an operating wavelength of an access network, forexample 1550 nm, with an adequate trade-off of optical properties.

A known solution would consist in using a standard multimode fiber thathas a refractive graded-index profile optimized for providing error-freetransmission with a broad bandwidth at a wavelength of 850 nm.Nevertheless, when a single-mode source operating at a wavelength of1550 nm is coupled to the standard multimode fiber, the optical signalinjected in the fiber stimulates, mainly but unfortunately not only thefundamental optical mode, but also the HOMs within the optical fiber.These HOMs induce modal noises that degrade the quality of opticaltransmission. There are actually two main categories of modal noises:incoherent and coherent noises.

Incoherent noise is based on the fact that, on the emitter side, theoptical signal coupled into the HOMs of the fiber may suffer from modaldispersion, and so since the different modes have different propagationdelay times and propagation constants, these HOMs may degrade thequality of optical transmission by overlapping delayed copies of themain optical signal on the receiver side. In practice, to perform wellin a high-bandwidth application, an optical fiber should have thehighest quality of optical transmission, which can be measured by meansof signal-to-noise ratio. For the incoherent contribution, thesignal-to-noise ratio, hereafter called “signal to incoherent noiseratio”, can be defined by the following equation:

$\begin{matrix}{{SNR}_{incoherent} = \frac{{\gamma }^{4}}{\sum\limits_{i}^{\;}{\beta_{i}}^{4}}} & (I)\end{matrix}$

wherein:|γ|² is the optical power coupled into the fundamental mode;|β_(i)|² is the optical power coupled into the higher order modes(HOMs), with i≧1.

Coherent noise is based on the fact that, the optical signal coupledinto the HOMs of the fiber on the emitter side may generate phasemismatch with the optical signal coupled into the fundamental mode,leading to uncontrolled interferometric recombinations into thefundamental mode on the receiver side. These interferences induceoptical power fluctuation that also degrades the quality of opticaltransmission. For the coherent contribution, the signal-to-noise ratio,hereafter called “signal to coherent noise ratio”, can be defined by thefollowing equation:

$\begin{matrix}{{SNR}_{coherent} = \frac{\left( {{\gamma }^{4} + {\underset{i}{\Sigma}{\beta_{i}}^{4}}} \right)}{\sigma_{coherent}}} & ({II})\end{matrix}$

wherein:|γ|² is the optical power coupled into the fundamental mode;|β_(i)|² is the optical power coupled into the higher order modes(HOMs), with i≧1;σ_(coherent) is a standard deviation coefficient of a Gaussian noise.

As a result, when less the optical power is coupled into the HOMs, theoptical transmission quality of the optical fiber is improved.

Due to the presence of these modal noises, such a standard multimodefiber is therefore not adapted to an interconnection with a single-modeoptical transmission system.

It would be therefore efficient to provide an optical fiber having abroad modal bandwidth at a wavelength of 850 nm and a significantreduced level of modal noises at a wavelength of 1310 nm or 1550 nm.

The Australian patent document AU 2002/100296 discloses an optical fibercomprising a single-mode core portion, which has a first refractiveindex, surrounded by a multimode core portion, which has a secondrefractive index, finally surrounded by a cladding which has a thirdrefractive index. The multi-portion index profile is arranged so thatthe fundamental mode is substantially matched to those of a single modefiber. However, this document does not provide any solution forminimizing modal noises caused by the HOMs of the optical fiber. Thedisclosed optical fiber further presents a relatively low modalbandwidth at 850 nm and requires a complex index profile design.

The French patent document FR 2 441 858 discloses an optical fiber witha central single-mode core and a multimode sheath for data transmission.In particular, the disclosed optical fiber does not exhibit agraded-index profile (the multimode fiber portion has a step-indexprofile), which does not allow meeting the requirements in terms of highmodal bandwidth at 850 nm. Nor does not address the problem of reductionof modal noises at a wavelength of 1310 nm or 1550 nm.

A solution to the problem of modal noises would be to reduce the corediameter of the multimode fiber. However reducing the optical corediameter leads to degrade the quality of multimode opticaltransmissions. Indeed, when a connection is carried out with a standardoptical fiber (i.e. a fiber having a diameter of 50 μm or 62.5 μm),optical transmission losses are even more important where the corediameter is low, thereby significantly limiting the modal bandwidth ofthe optical fiber for multimode optical transmissions. Therefore such asolution is not optimal.

SUMMARY OF THE INVENTION

In one particular embodiment of the invention an optical fiber isproposed comprising an optical core and an optical cladding surroundingthe optical core, the optical core having a refractive graded-indexprofile with a minimal refractive index n₁ and a maximal refractiveindex n₀, said optical fiber being such that it has a numerical apertureNA and an optical core radius a satisfying a criterion C of quality ofoptical communications defined by the following equation:

C = NA − 0.02 × a where:${{NA} = {\sqrt{n_{0}^{2} - n_{1}^{2}} = {{{n_{0} \cdot \sqrt{2\; \Delta}}{with}\mspace{14mu} \Delta} = \frac{n_{0}^{2} - n_{1}^{2}}{2\; n_{0}^{2}}}}},$

Δ is the normalized refractive index difference,and in that said minimal and maximal refractive indexes n₁, n₀ and saidoptical core radius a are chosen such that NA>0.20, a>10 μm and|C|<0.20.

Thus, by adapting the values of numerical aperture and core diameter inorder to satisfying a criterion of quality defined by theabove-mentioned equation, the invention provides a graded-index opticalfiber optimized for supporting both single-mode and multimodetransmissions with an adequate trade-off in terms of optical propertiesfor high-data rate applications.

To that end, the invention is based on the establishment of a trade-offbetween the core diameter and the numerical aperture of the opticalfiber allowing to significantly reduce incoherent and coherent modalnoises at single-mode wavelengths and to deliver a high modal bandwidthat multimode wavelengths. Indeed, the inventors discovered that the corediameter and numerical aperture of a graded-index optical fiber arestrongly correlated to both signal-to-coherent noise andsignal-to-incoherent noise ratios at single-mode transmissionwavelengths. It appears especially that decreasing the core diameterpromotes lower incoherent and coherent modal noises at single-modewavelengths and that increasing the numerical aperture of the opticalfiber unexpectedly leads to obtain a higher number of optical modes atmultimode wavelengths.

According to one advantageous characteristic, said minimal and maximalrefractive indexes n₁, n₀ and said optical core radius a are chosen suchthat |C|<0.10.

Coherent and incoherent modal noises are thus further reduced.

According to one more advantageous characteristic, said minimal andmaximal refractive indexes n₁, n₀ and said optical core radius a arechosen such that |C|<0.05.

Coherent and incoherent modal noises are even more reduced.

According to another advantageous characteristic, said minimal andmaximal refractive indexes n₁, n₀ and said optical core radius a arechosen such that C<0.

This promotes larger core radius.

Advantageously, said optical core radius is such that a>14 μm, and morepreferably a>19 μm, and even more preferably a=25 μm.

The quality of multimode optical transmissions is even more improved bylowering the splicing loss, for example, with standard diameter 50 μmmultimode optical fibers.

Advantageously, said minimal and maximal refractive indexes n₁, n₀ arechosen such that NA>0.25, more preferably NA>0.30, and even morepreferably NA>0.34.

According to a first particular embodiment, the refractive graded-indexprofile is a single alpha graded-index profile n(r) defined by thefollowing equation:

${n(r)} = {{{n_{0} \cdot \sqrt{1 - {2 \cdot \Delta \cdot \left( \frac{r}{a} \right)^{\alpha}}}}r} \leqq a}$

where:r is a variable representative of the radius of said optical fiber,α≧1, α being a non-dimensional parameter that defines the index profileshape of the optical core.

The optical fiber according to the invention is therefore simple tomanufacture and costs little, since all that is needed is to adaptdoping of the different fiber portions as a function of the desiredrefractive index profile satisfying to said criterion of quality.

According to a second particular embodiment, the optical core comprisesan inner optical core and an outer optical core surrounding the inneroptical core and the refractive graded-index profile is a twin alphagraded-index profile n(r) defined by the following equation:

${n(r)} = \left\{ {{\begin{matrix}{n_{1}^{\prime} \cdot \sqrt{1 - {2 \cdot \Delta_{1} \cdot \left( \frac{r}{a} \right)^{\alpha_{1}}}}} & {0 \leqq r \leqq r_{t}} \\{n_{2}^{\prime} \cdot \sqrt{1 - {2 \cdot \Delta_{2} \cdot \left( \frac{r}{a} \right)^{\alpha_{2}}}}} & {r_{t} \leqq r \leqq a}\end{matrix}{where}\text{:}\Delta_{1}} = {{\frac{\alpha_{2}{\Delta \left( \frac{r_{t}}{a} \right)}^{\alpha_{2} - \alpha_{1}}}{\alpha_{1} + {\left( {\alpha_{2} - \alpha_{1}} \right)\left( \frac{r_{t}}{a} \right)^{\alpha_{2}}}}\Delta_{2}} = {{\frac{\alpha_{1}\Delta}{{\left( {1 - {2\; \Delta}} \right) \cdot \left( {\alpha_{2} - \alpha_{1}} \right) \cdot \left( \frac{r_{t}}{a} \right)^{\alpha_{2}}} + \alpha_{1}}n_{1}^{\prime}} = {{\frac{n_{1}}{\sqrt{1 - {2\; \Delta}}}n_{2}^{\prime}} = {n_{1} \cdot \sqrt{\frac{{\left( {1 - {2\; \Delta}} \right) \cdot \left( {\alpha_{1} - \alpha_{2}} \right) \cdot \left( \frac{r_{t}}{a} \right)^{\alpha_{2}}} - \alpha_{1}}{\left( {1 - {2\; \Delta}} \right) \cdot \left( {{\left( {\alpha_{1} - \alpha_{2}} \right) \cdot \left( \frac{r_{t}}{a} \right)^{\alpha_{2}}} - \alpha_{1}} \right)}}}}}}} \right.$

r is a variable representative of the radius of said optical fiber,r_(t) is the radius of the inner optical core,n₁′ is the maximal refractive index of the inner optical core,n₂′ is the maximal refractive index of the outer optical core,Δ₁ is the normalized refractive index difference relative to the inneroptical core,Δ₂ is the normalized refractive index difference relative to the outeroptical core,α₁≧1, α₁ being a non-dimensional parameter that defines the indexprofile shape of the inner optical core,α₂≧1, α₂ being a non-dimensional parameter that defines the indexprofile shape of the outer optical core.

Thus, by minimizing the intermodal dispersion by means of a twin alphagraded-index profile, the modal bandwidth of the optical fiber atmultimode wavelengths is optimized, especially for the largest numericalapertures allowed by said criterion of quality of opticalcommunications.

In addition, the optical fiber in that alternative embodiment is simpleto manufacture and costs little, since all that is needed is to adaptdoping of the different fiber portions as a function of the desiredrefractive index profile satisfying to said criterion of quality.

According to one advantageous characteristic, the optical claddingcomprises a depressed trench surrounding the optical core or anengineered core-cladding interface.

A depressed trench-assisted optical fiber leads to decrease themacrobending losses by improving the confinement of the optical modeswithin the core. An engineered core-cladding solution aims to mitigatethe cladding effect and thus enlarge the modal bandwidth of the fiber.

In another embodiment, the invention pertains to an optical system, suchas an optical home network, comprising at least one optical fiberdescribed here above in any of its different embodiments.

This optical system may be an optical home network, such as a local areanetwork (LAN) and or a multi-dwelling unit (MDU) for example.

LIST OF FIGURES

Other features and advantages of embodiments of the invention shallappear from the following description, given by way of an indicative andnon-exhaustive examples and from the appended drawings, of which:

FIG. 1A graphically provides the refractive index profile of an opticalfiber according to a first embodiment of the invention;

FIG. 2A graphically provides the refractive index profile of an opticalfiber according to a second embodiment of the invention;

FIGS. 1B and 2B depict each a differential-mode-delay measurementcarried out on the optical fibers of FIGS. 1A and 2A respectively;

FIG. 3 graphically depicts the signal-to-incoherent noise ratio at awavelength of 1550 nm as a function of numerical aperture and coreradius of a graded-index optical fiber;

FIG. 4 graphically depicts the signal-to-coherent noise ratio at awavelength of 1550 nm as a function of numerical aperture and coreradius of a graded-index optical fiber;

FIG. 5 graphically depicts the signal-to-incoherent noise andsignal-to-coherent ratios at wavelengths of 1550 nm and 1310 nm as afunction of a criterion of quality of optical communications set inaccordance with the invention;

FIG. 6 graphically depicts the cumulative connection losses as afunction of numerical aperture and core radius of a graded-index opticalfiber;

FIG. 7 illustrates a schematic diagram used for measuring cumulativeconnection losses under multimode launch conditions defined in the“Encircled Flux” standard (IEC 61280-4-1);

FIG. 8 graphically illustrates the Encircled Flux template used forimplementing the schematic diagram of FIG. 7.

DETAILED DESCRIPTION

The general principle of the invention is to propose an optical fiberfor which the values of numerical aperture and core diameter are adaptedto support multimode operation up to a wavelength of 1550 nm with a highmodal bandwidth at a wavelength 850 nm for a 10 Gbps operation over longdistances (a few tens to a few hundreds of meters) and with reducedmodal noises when said optical fiber is coupled with standardsingle-mode fiber for reliable high speed transmission with single-modetransmission systems.

FIG. 1A depicts the refractive index profile n(r) of an optical fiberaccording to a first embodiment of the invention. It describes therelationship between the refractive index value n and the distance rfrom the center of the optical fiber.

In that first embodiment, the optical fiber is a graded-index opticalfiber having a refractive index profile n(r) defined as follow:

$\begin{matrix}{{n(r)} = \left\{ \begin{matrix}{n_{0} \cdot \sqrt{1 - {2 \cdot \Delta \cdot \left( \frac{r}{a} \right)^{\alpha}}}} & {r \leqq a} \\{n_{0} \cdot \sqrt{1 - {2 \cdot \Delta}}} & {r \geqq a}\end{matrix} \right.} & ({III})\end{matrix}$

where:r is a variable representative of the radius of the optical fiber,a is the optical core radius,Δ is the normalized refractive index difference, with

$\Delta = \frac{n_{0}^{2} - n_{1}^{2}}{2n_{0}^{2}}$

n₁ is the minimal refractive index of the optical core,n₀ is the maximal refractive index of the optical core,α is a non-dimensional parameter that defines the index profile shape ofthe optical core, which is chosen between 1.9 and 2.2 so as to providethe largest bandwidth at the target operating wavelength.

The optical fiber comprises, for 0≦r≦a, an optical core implementing asingle alpha graded-index profile and, for a≦r, an optical claddingdirectly surrounding the optical core and having a standard constantrefractive index. The alpha refractive index profile of the optical coreallows reducing intermodal dispersion of the optical fiber.

According to the invention, the optical core has a graded-index profilefor which the values of numerical aperture NA and core radius a(expressed in micrometers) are tuned so that they satisfy the followingequation:

C=NA−0.02×a  (IV)

where:NA is linked univocally to the normalized refractive index difference Δand the optical core's maximal refractive index n₀ as follows:

NA=√{square root over (n ₀ ² −n ₁ ²)}=n ₀·√{square root over (2Δ)}  (V)

a>10 μm,|C|<0.20, C being a real number, which represents a criterion of qualityof optical communications.

By adapting the values of numerical aperture NA and core diameter a inorder to satisfying the above equation (IV), the invention provides agraded-index optical fiber optimized for effectively reduce incoherentand coherent modal noises at single-mode wavelength of 1550 nm, whilekeeping a high modal bandwidth at multimode wavelength of 850 nm.

The inventors established that equation (IV) corresponds to apredetermined criterion of quality of optical communications thatensures supporting both single-mode and multimode transmissions with anadequate trade-off in terms of optical properties for high-data rateapplication. This criterion of quality has been obtained through anumerical assessment of the signal-to-incoherent noise ratio

${SNR}_{incoherent} = \frac{{\gamma }^{4}}{\underset{i}{\Sigma}{\beta_{i}}^{4}}$

and the signal-to-coherent noise ratio

${SNR}_{coherent} = \frac{\left( {{\gamma }^{4} + {\sum\limits_{i}{\beta_{i}}^{4}}} \right)}{\sigma_{coherent}}$

at a wavelength of 1550 nm as a function the core radius a and thenumerical aperture NA, as depicts in FIGS. 3 and 4.

The left-hand y-axis depicts the numerical aperture of the optical core(NA) and the x-axis depicts the optical core radius (a). The values ofSNR_(incoherent) (FIG. 3) and of SNR_(coherent) (FIG. 4) correspondingto a given pair of parameters (NA, a) are illustrated in shades of grayin the right-hand y-axis.

The inventors discovered that the core radius and numerical aperture ofa graded-index optical fiber are strongly correlated to bothsignal-to-coherent noise and signal-to-incoherent noise ratios at bothsingle-mode and multimode transmission wavelengths. Based on thisprinciple, SNR_(incoherent) and SNR_(coherent) have been simulated withvarious values of numerical aperture and core radius to establish arelationship allowing a significant reduction of modal noises atsingle-mode wavelength of 1550 nm, while delivering the broadest modalbandwidth at multimode wavelength of 850 nm. The criterion of qualityhas been derived from those numerical assessments assuming that, forvalues of core radius larger than 10 μm, SNR_(incoherent) andSNR_(coherent) shall be larger than 0 dB, and more preferentiallySNR_(incoherent) shall be approximately larger than 20 dB andSNR_(coherent) shall be approximately larger than 10 dB at thewavelength of 1550 nm.

It appears especially that decreasing core radius (a) and increasingnumerical aperture (NA) lead to promote higher SNR_(incoherent) andSNR_(coherent) at 1550 nm. It further appears that the greater thenumerical aperture is, the more the core radius to set can be relativelyhigh: by doing this, multimode optical transmissions can be optimized tomeet the demands of high-bandwidth applications (typically 10 Gbps) overlong distances (a few tens to a few hundreds of meters), such as in theEthernet high speed transmission networks.

As a strictly illustrative example (and therefore of a non-limitingnature), the optical core radius a illustrated in FIG. 1 is about 19 μmand the numerical aperture NA is about 0.297, thereby satisfying thecriterion of quality of optical communications established in complyingwith the invention. The parameter α of the optical core's index profileis about 2.065 and the normalized refractive index difference Δ is about2% (n₁ being approximately equal to 1.457 and n₀ approximately equal to1.487).

The advantages of the invention will be more evident by comparingoptical fibers of the prior art with an exemplary optical fiberaccording to the invention. Table 1 below shows values of the coreradius and numerical aperture of a standard graded-index optical fibersand value of the criterion C of quality that would be obtained by usingthe above equation (IV). That prior art fibers are subjected to anoptical signal of a wavelength λ of 850 nm for the high-speed networks.

TABLE 1 a (μm) NA C (a, NA) 25 0.200 −0.30 31.25 0.275 −0.35 40 0.290−0.51 25 0.290 −0.21

The graph of FIG. 5 depicts the signal-to-incoherent noise andsignal-to-coherent ratios at wavelengths of 1550 nm and 1310 nm as afunction of the quality criterion C discussed above in relation withFIGS. 1, 3, 4 and applied both to graded-index optical fibers of priorart and optical fibers of the invention. The y-axis depictsSNR_(incoherent) and SNR_(coherent) (in dB) and the x-axis depictsdifferent values of the criterion C of quality comprised between −0.60and 0.20.

It can be observed that none of the optical fibers of prior art owns acore index profile that allows meeting the criterion C of quality of theinvention |C|<0.20, which consequently is reflected by lower values ofSNR compared to those resulting from the invention. This graph showsthat the model according to the invention leads to the establishment ofa good quality criterion.

In addition, in order to further improve SNR_(incoherent) andSNR_(coherent), the criterion of quality can be set advantageously suchas |C|<0.10 (i.e. |NA−0.02×a|<0.10), and more advantageously such as|C|<0.05 (i.e. |NA−0.02×a|<0.05), preferably with C<0. It can be seenthat these signal-to-noise radios are maximized when the value of C isclose to 0.

According to one advantageous characteristic, the index profile of theoptical fiber of FIG. 1 can comprise a depressed-index portion (notshown on FIG. 1) located between the graded-index core and the cladding.This depressed-index portion, also called a depressed trench, has anegative refractive index difference with respect to the optical fibercladding, and its position and size are designed so as to improvebend-loss resistance of multimode fiber.

FIG. 2A graphically provides the refractive index profile n(r) of anoptical fiber according to a second embodiment of the invention.

In that second embodiment, the optical fiber exhibits an optical coreconsisted of two portions, an inner optical core and an outer opticalcore surrounding the inner optical core, and the refractive graded-indexprofile is a twin alpha graded-index profile n(r) defined by thefollowing equation:

$\begin{matrix}{{n(r)} = \left\{ {{\begin{matrix}{n_{1}^{\cdot \prime} \cdot \sqrt{1 - {2 \cdot \Delta_{1} \cdot \left( \frac{r}{a} \right)^{\alpha_{1}}}}} & {0 \leqq r \leqq r_{t}} \\{n_{2}^{\prime} \cdot \sqrt{1 - {2 \cdot \Delta_{2} \cdot \left( \frac{r}{a} \right)^{\alpha_{2}}}}} & {r_{t} \leqq r \leqq a} \\{n_{1}^{\prime} \cdot \sqrt{1 - {2 \cdot \Delta}}} & {a < r}\end{matrix}{where}\text{:}\Delta_{1}} = {{\frac{\alpha_{2}{\Delta \left( \frac{r_{t}}{a} \right)}^{\alpha_{2} - \alpha_{1}}}{\alpha_{1} + {\left( {\alpha_{2} - \alpha_{1}} \right)\left( \frac{r_{t}}{a} \right)^{\alpha_{2}}}}\Delta_{2}} = {{\frac{\alpha_{1}\Delta}{{\left( {1 - {2\; \Delta}} \right) \cdot \left( {\alpha_{2} - \alpha_{1}} \right) \cdot \left( \frac{r_{t}}{a} \right)^{\alpha_{2}}} + \alpha_{1}}n_{1}^{\prime}} = {{\frac{n_{1}}{\sqrt{1 - {2\; \Delta}}}n_{2}^{\prime}} = {n_{1} \cdot \sqrt{\frac{{\left( {1 - {2\; \Delta}} \right) \cdot \left( {\alpha_{1} - \alpha_{2}} \right) \cdot \left( \frac{r_{t}}{a} \right)^{\alpha_{2}}} - \alpha_{1}}{\left( {1 - {2\; \Delta}} \right) \cdot \left( {{\left( {\alpha_{1} - \alpha_{2}} \right) \cdot \left( \frac{r_{t}}{a} \right)^{\alpha_{2}}} - \alpha_{1}} \right)}}}}}}} \right.} & ({VI})\end{matrix}$

r is a variable representative of the radius of said optical fiber,a is the optical core radius comprising both inner and outer opticalcores,r_(t) is the radius of the inner optical core,n₁′ is the maximal refractive index of the inner optical core,n₂′ is the maximal refractive index of the outer optical core,Δ₁ is the normalized refractive index difference relative to the inneroptical core,Δ₂ is the normalized refractive index difference relative to the outeroptical core,α₁≧1, α₁ being a non-dimensional parameter that defines the indexprofile shape of the inner optical core,α₂≧1, α₂ being a non-dimensional parameter that defines the indexprofile shape of the outer optical core.

The respective parameters Δ₁, Δ₂ and n₁′, n₂′ ensure the continuity ofthe refractive index profile and its first derivative at the transitionfrom the inner core to the outer core.

That particular twin alpha index profile offers the advantage of beingable to improve even more the modal bandwidth of the optical fiber atmultimode wavelengths.

All that has been said so far in relation with FIG. 1A, 3 to 5 about thecriterion of quality applies mutatis mutandis to that second embodimentof the invention. Also, in order to further improve the modal bandwidthof the optical fiber, the fiber according to second embodiment cancomprise a depressed trench as described above in accordance withexplanation provided in FIG. 5.

As a strictly illustrative example (and therefore of a non-limitingnature), the optical core radius a illustrated in FIG. 2A is about 19 μmand the numerical aperture NA is about 0.297, thereby satisfying thecriterion of quality of optical communications established in complyingwith the invention. The parameters α₁ and α₂ of the optical core's indexprofile are respectively about 2.0851 and 2.0433. The radius of theinner optical core (r_(t)) is about 0.5 μm.

FIGS. 1B and 2B graphs depict each a differential-mode-delay measurement(hereafter called “DMD measurement”) (e.g. as set forth in the FOTP-220standard) carried out on the optical fibers of FIGS. 1A and 2Arespectively. This kind of graph is obtained by successively injectinginto the multimode optical fiber a light pulse having a given wavelengthwith a radial offset between each successive pulse. Delay of each pulseis then measured after a given length of fiber. Multiple identical lightpulses are injected with different radial offsets with respect to thecenter of the optical core's core. The y-axis depicts the radial offset(noted “radial launch” on the Figure) in micrometers with respect to thecenter of the optical core's core and the x-axis depicts the time innanoseconds. From these DMD measurements, it is possible to determinethe effective modal bandwidth of the optical fiber. It appears fromgraphs 1B and 2B that the optical fibers of the invention present a timelag between the pulses propagating along different radial offsets whichis relatively low, resulting in broad modal bandwidth. Furthermore, onecan see the advantage of the twin alpha graded-index profile (FIG. 2B),which depicts differential-mode-delay measurements narrower than that ofthe single alpha graded-index profile (FIG. 1B), therefore has bettermodal bandwidths.

It should be noted that the DMD measurements carried out with a radialoffset upper than 18 μm are not relevant. In particular it can beobserved a few multiple pulses on the left-hand graph caused by claddingeffect.

FIG. 6 depicts the cumulative connection losses as a function ofnumerical aperture and core radius of a single alpha graded-indexoptical fiber.

The left-hand y-axis depicts the numerical aperture of the optical core(NA) and the x-axis depicts the optical core's radius (a). The values ofcumulative connection losses (expressed in dB) corresponding to a givenpair of parameters (NA, a) are illustrated in shades of gray in theright-hand y-axis.

Cumulative connection losses are measured at a wavelength of 850 nmunder multimode launch conditions for measuring attenuation defined inthe known “Encircled Flux” standard (IEC 61280-4-1). Principle of launchconditions defined by the EF is reminded in FIG. 8. EF defines theintegral of power output of the optical fiber over the radius of thefiber.

As illustrated in FIG. 7, to characterize cumulative connection lossesin accordance with EF standard conditions, an optical fiber 70 accordingto the invention is subject to a spot of a multimode light source 71coupled to thereon. The near field pattern of the spot is then observedat the output of the optical fiber by a receiver 72 and post-processedto assess the cumulative connection losses at P1 and P2 levels. In otherwords, “cumulative connection losses” means losses measured cumulativelyat connections P1 and P2.

It appears from FIG. 6 that, for acceptable cumulative losses, theoptical core radius a shall be upper than 20 μm. If one choose thecriterion of quality C be such that |C|<0.10 for example, the numericalaperture shall be upper than 0.30. With such values, the numericalaperture NA and optical core radius a satisfy the criterion C of qualityas defined according to the above equation (IV). To complete theillustration of FIG. 6, a few complementary values of core radius a,numerical aperture NA and criterion C applied for optical fibers incompliance with the invention are showed in the Table 2 below andcompared with cumulative losses measured.

TABLE 2 Cumulative a (μm) NA C (a, NA) Loss (dB) 24 0.28 −0.20 1.0 190.28 −0.10 2.2 16.5 0.28 −0.05 3.1 27.5 0.35 −0.20 1.0 22.5 0.35 −0.101.4 20 0.35 −0.05 1.8

It becomes apparent that, for values of NA of 0.35, the optical fibersof the invention allow larger core radius than that for which values ofNA is 0.28, which enables to obtain reduced cumulative losses.

Finally, in addition to improve the signal-to-noise ratios, increasingnumerical aperture of the optical fiber leads to obtain a higher numberof optical modes at multimode wavelengths. The number of optical modesguided in the fiber is function of the numerical aperture and opticalcore radius. In particular the number of guided optical modes can beendetermined by means of the following equation:

$N = {\frac{\alpha}{\alpha + 2} \cdot a^{2} \cdot \left( \frac{2\pi}{\lambda} \right)^{2} \cdot n_{0}^{2} \cdot \Delta}$

wherein:a is the optical core radius,Δ is the normalized refractive index difference, with

$\Delta = \frac{n_{0}^{2} - n_{1}^{2}}{2\; n_{0}^{2}}$

α is a non-dimensional parameter that defines the index profile shape ofthe optical core, comprised between 1.9 and 2.2,N is the number of optical modes.

An exemplary embodiment of the present application overcomes thedifferent drawbacks of the prior art.

More specifically, an exemplary embodiment provides an optical fiberoptimized for supporting both single-mode and multimode transmissionswith an adequate trade-off in terms of optical properties for high-datarate applications.

An exemplary embodiment provides an optical fiber that offers thebroadest modal bandwidth for multimode transmission over long distancesand that sustains a fundamental mode similar to that required forsingle-mode transmission.

An exemplary embodiment provides an optical fiber that significantlyreduces modal noises at wavelengths of 1310 nm and 1550 nm, whiledelivering a broad modal bandwidth at a wavelength of 850 nm.

An exemplary embodiment provides an optical fiber that is simple tomanufacture and costs little.

Although the present disclosure has been described with reference to oneor more examples, workers skilled in the art will recognize that changesmay be made in form and detail without departing from the scope of thedisclosure and/or the appended claims.

1. An apparatus comprising: a home optical data network formed of anoptical fiber comprising: an optical core; and an optical claddingsurrounding the optical core, the optical core having a refractivegraded-index profile with a minimal refractive index n₁ and a maximalrefractive index n₀; and said optical fiber having a numerical apertureNA and an optical core radius a satisfying a criterion C of quality ofoptical communications defined by the following equation:C = NA − 0.02 × a where:${{NA} = {\sqrt{n_{0}^{2} - n_{1}^{2}} = {{{n_{0} \cdot \sqrt{2\; \Delta}}{with}\mspace{14mu} \Delta} = \frac{n_{0}^{2} - n_{1}^{2}}{2\; n_{0}^{2}}}}},$Δ is the normalized refractive index difference, and wherein saidminimal and maximal refractive indexes n₁, n₀ and said optical coreradius a are chosen such that NA>0.20, a>10 μm and |C|<0.20.
 2. Theapparatus according to claim 1, wherein said minimal and maximalrefractive indexes n₁, n₀ and said optical core radius a are chosen suchthat |C|<0.10.
 3. The apparatus according to claim 1, wherein saidminimal and maximal refractive indexes n₁, n₀ and said optical coreradius a are chosen such that |C|<0.05.
 4. The apparatus according toclaim 1, wherein said minimal and maximal refractive indexes n₁, n₀ andsaid optical core radius a are chosen such that C<0.
 5. The apparatusaccording to claim 1, wherein said optical core radius is such that a>14μm.
 6. The apparatus according to claim 1, wherein said minimal andmaximal refractive indexes n₁, n₀ are chosen such that NA>0.25.
 7. Theapparatus according to claim 1, wherein the refractive graded-indexprofile is a single alpha graded-index profile n(r) defined by thefollowing equation:${n(r)} = {{{n_{0} \cdot \sqrt{1 - {2 \cdot \Delta \cdot \left( \frac{r}{a} \right)^{\alpha}}}}r} \leqq a}$where: r is a variable representative of the radius of said opticalfiber, α≧1, α being a non-dimensional parameter that defines the indexprofile shape of the optical core.
 8. The apparatus according to claim1, wherein the optical cladding comprises a depressed trench surroundingthe optical core.
 9. The apparatus of claim 1, further comprising: amultimode light source coupled to the optical fiber; and a receivercoupled to the optical fiber.
 10. A method comprising: forming a homeoptical data network with an optical fiber comprising: an optical core;and an optical cladding surrounding the optical core, the optical corehaving a refractive graded-index profile with a minimal refractive indexn₁ and a maximal refractive index n₀; and said optical fiber having anumerical aperture NA and an optical core radius a satisfying acriterion C of quality of optical communications defined by thefollowing equation: C = NA − 0.02 × a where:${{NA} = {\sqrt{n_{0}^{2} - n_{1}^{2}} = {{{n_{0} \cdot \sqrt{2\; \Delta}}{with}\mspace{14mu} \Delta} = \frac{n_{0}^{2} - n_{1}^{2}}{2\; n_{0}^{2}}}}},$Δ is the normalized refractive index difference, and wherein saidminimal and maximal refractive indexes n₁, n₀ and said optical coreradius a are chosen such that NA>0.20, a>10 μm and |C|<0.20; andtransmitting data over the optical fiber.
 11. The method of claim 10,wherein transmitting data comprises transmitting a multimode opticalsignal over the optical fiber.
 12. The method of claim 10, whereintransmitting data comprises transmitting a single mode optical signalover the optical fiber.
 13. The method of claim 10, wherein transmittingdata comprises transmitting both single mode and multimode opticalsignals over the optical fiber.
 14. The method according to claim 10,wherein said minimal and maximal refractive indexes n₁, n₀ and saidoptical core radius a are chosen such that |C|<0.10.
 15. The methodaccording to claim 10, wherein said minimal and maximal refractiveindexes n₁, n₀ and said optical core radius a are chosen such that|C|<0.05.
 16. The method according to claim 10, wherein said minimal andmaximal refractive indexes n₁, n₀ and said optical core radius a arechosen such that C<0.
 17. The method according to claim 10, wherein saidoptical core radius is such that a>14 μm.
 18. The method according toclaim 10, wherein said minimal and maximal refractive indexes n₁, n₀ arechosen such that NA>0.25.
 19. The method according to claim 10, whereinthe refractive graded-index profile is a single alpha graded-indexprofile n(r) defined by the following equation:${n(r)} = {{{n_{0} \cdot \sqrt{1 - {2 \cdot \Delta \cdot \left( \frac{r}{a} \right)^{\alpha}}}}r} \leqq a}$where: r is a variable representative of the radius of said opticalfiber, α≧1, α being a non-dimensional parameter that defines the indexprofile shape of the optical core.
 20. The method according to claim 10,wherein the optical cladding comprises a depressed trench surroundingthe optical core.